Unitarity and Monojet Bounds on Models for DAMA, CoGeNT, and CRESST-II

TL;DR

The paper shows that enforcing a collider-level contact interaction for DM–quark couplings leads to a perturbative unitarity bound on the mediator scale $\Lambda$ that is stronger than MET constraints, casting doubt on a universal contact description for the DAMA/CoGeNT/CRESST-II signals. It then analyses light $Z'$ mediator scenarios, deriving how monojet searches constrain the parameter space across regimes where the mediator is light and either on- or off-shell with respect to DM, concluding that Tevatron data currently provide the strongest bounds for $m_{Z'}\lesssim 100$ GeV while the LHC predominates at higher masses. The study translates collider bounds into direct-detection cross sections, finding that only narrow, on-shell $Z'$ scenarios with $Z'\rightarrow X\bar{X}$ can meaningfully impact the DAMA/CoGeNT/CRESST regions. Overall, the work emphasizes that collider consistency (unitarity) and direct-detection anomalies together favor mediator-accessible, UV-complete descriptions over simple contact operators.

Abstract

If dark matter interacts with quarks or gluons, the mediator of these interactions is either directly accessible at the LHC or is so heavy that its effects are encoded in contact operators. We find that the self-consistency of a contact operator description at the LHC implies bounds on the mediator scale stronger than those found from missing energy searches. This translates into spin-independent elastic scattering cross-sections at a level < 10^-41 cm^2, with direct implications for the DAMA, CoGeNT, and CRESST-II anomalies. We then carefully explore the potential of monojet searches in the light mediator limit, focusing on a Z' model with arbitrary couplings to quarks and dark matter. We find that the Tevatron data currently provides the most stringent bounds for dark matter and Z' masses below 100 GeV, and that these searches can constrain models for the DAMA, CoGeNT, and CRESST-II anomalies only if the mediator can decay to a pair of dark matter particles.

Figures (4)

• Figure 1: Here we compare the monojet rate coming from the contact operator ${\cal O}$ ($\sigma_{contact}$) to that of a $Z'$ model ($\sigma$) with the $Z'$ coupling equally to quarks and dark matter. In both models we turn on only couplings to left-handed up quarks and dark matter and set $m_X=10$ GeV. In comparing the two models we fix $\Lambda = m_{Z'}/g$, such that their low-energy predictions agree. The shaded, strongly coupled region $g^{2} > 4 \pi/\sqrt{3}$ represents the unitarity constraint of the UV model.
• Figure 2: Here we compare the direct detection upper bounds obtained from ATLAS monojets DM2DM3Coolest (solid blue) and the unitarity constraint (\ref{['contactbound']}) with $E =$ 7 TeV (solid red line). We have also included the optimistic $5 \sigma$ LHC reach at 14 TeV DM2 (dashed blue) along with the unitarity bound, at $E =$ 14 TeV (dashed red). All bounds are derived under the assumption that the quark-DM interaction ${\cal O}$ remains contact at LHC energies and with universal quark coupling. For reference we include the DAMA $3\sigma$Bernabei:2008yiSavage:2008er, CoGeNT 90$\%$ CL Aalseth:2011wp, and CRESST-II 1$\sigma$ and $2\sigma$ preferred regions Angloher:2011uu as well as the 90$\%$ CL XENON-100 bound Aprile:2011hi.
• Figure 3: Upper bounds on $\sqrt{g_{d} g_{X}}$ as a function of the DM mass when $m_{Z'} < 2 m_{X}$, with $m_{Z'} \ll 2m_{X}$ (solid lines), and $m_{Z'} =100$, 500 GeV (dashed lines). CDF provides the strongest bounds when the DM mass is less than about 30 GeV. Note that the value of the mediator mass only matters near threshold $m_{Z'} \sim 2 m_{X}$, where the effect of the $Z'$ width is also relevant.
• Figure 4: $95\%$ CL monojet bounds on the $Z'$ model from CDF and ATLAS in the low DM mass and heavy DM regimes (see the text for more details). The bounds are derived assuming that a single quark coupling at a time is switched on. In Eq. (\ref{['gen']}) we show how to modify the bounds in the most general case. As a reference we also quote the bound arising from the assumption of universal coupling. The "plus" signs indicate the region were the CDF and ATLAS bounds cross each other (see also Fig. \ref{['plot0']}).